Test 8 Review: domain/range/continuous/discrete

Front

What is the definition of 'domain' in a function?

Back

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

Front

What is the definition of 'range' in a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What does it mean for a function to be 'continuous'?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph; it can be drawn without lifting the pencil.

Front

What does it mean for a function to be 'discrete'?

Back

A function is discrete if it consists of distinct or separate values, often represented as individual points on a graph.

Front

How do you find the range of a function from its graph?

Back

To find the range, identify the lowest and highest y-values that the graph reaches.

Front

What is the domain of the function h(x) = x^2 + 3?

Back

The domain is all real numbers, as any real number can be squared and added to 3.

Front

If f(x) = 2x + 1, what is f(-4)?

Back

f(-4) = 2(-4) + 1 = -8 + 1 = -7.

Front

What is the range of the function f(x) = x^2?

Back

The range is all real numbers y such that y >= 0, since x^2 is always non-negative.

Front

How do you determine the domain of a set of points?

Back

The domain is the set of all x-values from the given points.

Front

What is the significance of the notation y > -1 in terms of range?

Back

It indicates that the range includes all y-values greater than -1, but not -1 itself.